Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii

Banas L, Prohl A, Schätzle R (2010)
Numerische Mathematik 115(3): 395-432.

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We prove the existence of weak solutions to the harmonic map heat flow, and wave maps into spheres of nonconstant radii. Weak solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite elements, where discrete Lagrange multipliers are employed to exactly meet the sphere constraint at mesh-points. Computational studies are included to motivate interesting dynamics in two and three spatial dimensions.
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Banas L, Prohl A, Schätzle R. Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. Numerische Mathematik. 2010;115(3):395-432.
Banas, L., Prohl, A., & Schätzle, R. (2010). Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. Numerische Mathematik, 115(3), 395-432. doi:10.1007/s00211-009-0282-y
Banas, L., Prohl, A., and Schätzle, R. (2010). Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. Numerische Mathematik 115, 395-432.
Banas, L., Prohl, A., & Schätzle, R., 2010. Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. Numerische Mathematik, 115(3), p 395-432.
L. Banas, A. Prohl, and R. Schätzle, “Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii”, Numerische Mathematik, vol. 115, 2010, pp. 395-432.
Banas, L., Prohl, A., Schätzle, R.: Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. Numerische Mathematik. 115, 395-432 (2010).
Banas, Lubomir, Prohl, Andreas, and Schätzle, Reiner. “Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii”. Numerische Mathematik 115.3 (2010): 395-432.
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